As education constitutes an essential development standard for individuals and societies, researchers have been exploring the use of artificial intelligence (AI) in this domain and have embedded the technology within it through a myriad of applications. In order to provide a detailed overview of the efforts, this article pays particular attention to these developments by highlighting key application areas of data-driven AI in education; it also analyzes existing tools, research trends, as well as limitations of the role data-driven AI can play in education. In particular, this article reviews various applications of AI in education including student grading and assessments, student retention and drop-out predictions, sentiment analysis, intelligent tutoring, classroom monitoring, and recommender systems. This article also provides a detailed bibliometric analysis to highlight the salient research trends in AI in education over nine years (2014-2022) and further provides a detailed description of the tools and platforms developed as the outcome of research and development efforts in AI in education. For the bibliometric analysis, articles from several top venues are analyzed to explore research trends in the domain. The analysis shows sufficient contribution in the domain from different parts of the world with a clear lead for the United States. Moreover, students' grading and evaluation have been observed as the most widely explored application. Despite the significant success, we observed several aspects of education where AI alone has not contributed much. We believe such detailed analysis is expected to provide a baseline for future research in the domain.